Im not using menu bar in my design but I need to use the Forum search to include it in my foro pages.
Is there a shortcode to include the search box in the place that I choose?
if you use some page builder then you can add wpForo Search widget in any place of your page. wpForo has a widget with forum search field, so it can be located wherever you want.
"https://asoal.it/community/forum/" is somehow wrong. It should be one of them, or whatever name you select.